Metropolis-hastings sampling
Metropolis-Hastings sampling is a Markov chain Monte Carlo method that proposes state changes and accepts or rejects them probabilistically to generate samples from a target distribution.
Fabulous Adventures in Data Structures and Algorithms
The Metropolis algorithm is a Markov chain Monte Carlo method that generates samples from a target distribution using proposed moves and acceptance probabilities based on relative weights.
- How it is used
- Generates samples from continuous posterior distributions when their non-normalized weight functions are available but direct sampling is not.
- How deep it goes
- Works through the acceptance rule and a one-dimensional C# implementation, while leaving multidimensional implementation aside.
- Examples
- Uses a weighted coin-flip transition, a two-peaked target histogram, and a coin-fairness posterior after nine heads in ten flips.
- What you can do after
- Build it from scratch in C# to sample a supplied target weight function or a continuous posterior.
Machine Learning Algorithms in Depth
Metropolis-Hastings sampling is a Markov chain Monte Carlo technique that proposes state changes and accepts or rejects them using a probability designed to preserve the target distribution.
- How it is used
- Constructs samples from high-dimensional target distributions when direct sampling is difficult.
- How deep it goes
- Derives the acceptance correction from detailed balance and implements the complete proposal, evaluation, and decision loop.
- Examples
- Demonstrates a multivariate Gaussian-mixture target with a multivariate normal proposal and a Python sampler implementation.
- What you can do after
- Build a Metropolis-Hastings sampler from scratch and apply it to a multivariate Gaussian mixture.
Read how Machine Learning Algorithms in Depth explains metropolis-hastings sampling →
Related concepts
- markov chain monte carlokind of · Markov chain Monte Carlo is a family of sampling algorithms that generate samples using a Markov chain whose stationary or limiting distribution is a target probability distribution.
- proposal distributionuses · A proposal distribution is a probability distribution from which a sampling or inference algorithm generates candidate states or samples.
- initial state distributionuses · An initial state distribution is a probability distribution over the states from which a stochastic process or episode begins.
- accept/reject algorithmuses · An accept-reject algorithm samples candidate outcomes from a proposal process and accepts or rejects them according to a specified rule or probability.
- Markov chainimplements · A Markov chain is a stochastic process of states whose transition probabilities depend on the current state rather than the full preceding history.
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